Electric vehicle battery chemistry affects supply chain disruption vulnerabilities

We examine the relationship between electric vehicle battery chemistry and supply chain disruption vulnerability for four critical minerals: lithium, cobalt, nickel, and manganese. We compare the nickel manganese cobalt (NMC) and lithium iron phosphate (LFP) cathode chemistries by (1) mapping the supply chains for these four materials, (2) calculating a vulnerability index for each cathode chemistry for various focal countries and (3) using network flow optimization to bound uncertainties. World supply is currently vulnerable to disruptions in China for both chemistries: 80% [71% to 100%] of NMC cathodes and 92% [90% to 93%] of LFP cathodes include minerals that pass through China. NMC has additional risks due to concentrations of nickel, cobalt, and manganese in other countries. The combined vulnerability of multiple supply chain stages is substantially larger than at individual steps alone. Our results suggest that reducing risk requires addressing vulnerabilities across the entire battery supply chain.

By definition, all companies producing their own battery cells, either in-house or through joint ventures or partnerships, are actively deciding the battery chemistries they have in their vehicle batteries, and thus where they source their battery cathode material from and the risks they might face due to global trade.Additionally, some companies (e.g.Ford, 9 GM, 10 Tesla 11 ) have signed agreements with raw materials producers to supply their joint ventures and/or in-firm production, but may or may not directly control the exact sources of these materials, which may slightly muddy the clear delineations described in the table above.Some companies with lesser control may still choose to source batteries specifically because of the battery chemistry, but since they have no direct control, they also have less direct control over their exposure to risk from the upstream material supply chains.

Supplementary Text S1-2. Mineral Criticality Discussion and Other Trade-offs in Battery Design Choices
3][14] However, other materials that are sometimes considered 'critical' can be used cathode materials and/or batteries writ large, such as graphite, aluminum, phosphorus, copper, and fluorine.We summarize various perspectives on mineral criticality in Table A2-1, with a more general discussion of mineral criticality and how to measure it in Supplementary Text S2.The primary reason for this non-or less-critical categorization seems to be because the relative demand for such materials in batteries is small relative to the overall size of the market, and the number of countries that supply the material is high, as seen in Table A2-2.In general, if demand for the aforementioned minerals -or new minerals due to development of novel chemistries -becomes significant and/or are included on critical mineral lists, especially those related to batteries or energy technologies, then more detailed analysis would be useful in better understanding the vulnerabilities present in their supply chains.While we focus on Lithium, Cobalt, Nickel, and Manganese due to a general understanding that these are the most critical materials at the current moment and the fact that there exists sufficient data for these materials, likely due to their status as the most critical minerals, other materials that are not yet considered as critical typically have data issues, making it challenging to apply the full analysis method we have suggested here.
We take for example the mineral phosphorus, which in Table A2-1 is considered to be critical in some contexts, like other minerals excluded from the main body of the paper.Given that the criticality of phosphorus in the electric vehicle lithium ion battery context is uncertain, we provide a Sankey diagram in Supplementary Fig. 3, though data limitations prevent us from understanding country-level production of phosphoric acid that could be used as a precursor to LFP.We find demand for phosphorus for LFP production was 17,500 metric tons, as compared to the roughly 30 million metric tons of phosphorus mined in 2020 (223 Mt of phosphate rock) 15 -roughly 0.06% of total worldwide phosphorus demand.Even when narrowing down the phosphorus supply chain to phosphoric acid production, the primary precursor for the phosphorus used in LFP batteries, 16 this corresponds to roughly 0.075% of phosphoric acid demand.According to the USGS, 17 15 Based on their analysis, they explicitly state that "we do not believe that phosphorus is as critical a raw material from a known reserves perspective as other battery elements…"    currently reasonably economically extractable material) around the world in 2020.While we recognize it is currently non-economical to convert most of these phosphorus resources (and indeed, nickel, cobalt, and manganese, to a certain extent) to the high level of quality and purity required for LFP batteries, in the vein of the Simon-Erlich wagers, we suggest that massive growth in market demand for such materials will encourage a shift in developing lower-grade resources for such applications and technological advancement to allow for such development.
With the massive projected growth of all minerals due to the expansion of battery supply chains and the overall energy transition, we suggest that further efforts to gather better data and make such data available to researchers and analysts will be necessary to address future concerns.
Supplementary Fig. 3.A Sankey diagram for global flows of phosphorus that available data suggest are involved in battery material supply chains.
See Supplementary Text S3-2 for further details and data sources.Note the scale of production -approximately 28 million tons of phosphorus (contained phosphorus) was extracted in 2020.
We note Supplementary Fig. 3 displays regional production data of phosphoric acid, the primary precursor used in LFP battery cathodes, as this level of aggregation was the most detailed that was publicly available. 30As a result, we can only compare demand phosphorus used for LFP production to trade of phosphoric acid, and also cannot calculate a full vulnerability Cobalt has been associated with child labor and heavy environmental damage in the Democratic Republic of the Congo. 14,31Thus, while we simplify calculations of vulnerability to one dimension of supply availability, we recognize that tradeoffs exist in multiple dimensions across these four materials.
Lithium ion batteries themselves are composed of four primary components: a lithium compound cathode, graphitic carbon anode, liquid electrolyte, and polymer-based separator, as well as various other structural elements (e.g.copper and/or aluminum current collectors).There are some possible alternatives for electrolyzers, separators, and anode materials, but the diversity of choices in these are much fewer (e.g.anodes are currently made with graphite, with only some possibility for partial substitution with silicon), 32 [32][33][34] While Sodium Ion batteries have been developed for electric vehicles in China, 35 market penetration is currently low and the cathode materials often contain some mix of nickel, cobalt, and/or manganese, as well as other minerals such as titanium or copper, which does not fully remove the risks discussed in this article.
Beyond the critical materials required for each chemistry, other trade-offs exist -LFP battery pack energy densities are anywhere from 50 to 85% of that of NMC battery packs 33,36,37 while being 105% to 85% of the cost of production. 13,38Thus, to achieve a battery with a certain amount of energy, differing amounts of critical materials would be required to build a battery of each type.

Supplementary Text S2. Literature Review
Supplementary Table 5.A summary of existing key literature on EV battery material supply chain vulnerabilities.We recognize that studies with these methods and themes could be used in the context of EV battery materials, but in some cases have not been applied in such a manner.To answer our research question, we need to build a model that maps the battery material supply chains at a national level and measures interactions between trade flows and production capacity, while accounting for uncertainty and missing data.Several streams of literature have investigated relevant concepts and metrics, including literature on energy security, materials criticality, material flow analysis, input-output analysis, and supply chain disruption propagation.
The relationship between our model and these literature streams is summarized in Supplementary Table 5.
Energy security debates have long focused on where energy resources are sourced, with definitions often made in terms of access to fuels or security of supply, largely in the context of oil and other fossil resources. 55,5641][42]57 However, transitions to renewable and electricity-based systems have introduced new geographical dependencies that differ from those raised by fossil fuels. 44,58,59The materials criticality literature was in part developed to address these nuances.
The literature on materials criticality attempts to assess the relative risks and vulnerabilities associated with the supply of minerals and materials.1][62] These aggregated metrics have been applied across multiple battery supply chains and battery chemistries, particularly from the perspective of import dependence, rather than the relative impact of various countries' involvement in supply chains.For example, some studies 12,20,43 measure concentration of production with the Herfindahl-Hirschman Index and then weight them (using indices such as the World Governance Indicators, material demand, import reliance, etc.) to account for different levels of risk.For example, the first of these studies 12 aggregates four measures of risk for battery-related critical minerals in the context of various cathode material compositions, finding that in a simple arithmetic mean aggregation, LFP is the only battery chemistry with "measurably lower supply risk compared to the other battery types."While these metrics can capture a broad range of concerns, they may mask the dimensions that are important for ensuring supply availability throughout a specific product's entire supply chain, 63,64 including obfuscating the vulnerability of risk caused by specific countries.In the case of battery materials, while we learn that lithium and cobalt tend to be 'more critical' than other battery minerals, we suggest that these measurements do not adequately describe the importance of specific countries and their trade inter-dependencies, especially in the context of battery material chemistry choices and their supply chains.
The material flow analysis literature maps and characterizes the production and flow of materials using international trade data and various sources of production data to better understand geographical relationships of supply chains.In the context of battery materials, some of this literature focuses on specific stages of the value chain, e.g.raw materials and mining, while others encompass all steps.Most of these trace specific materials at a global context, such as lithium, 1 cobalt, 2,46 nickel, 47 and manganese. 65Additional studies have considered all of the cathode materials in a regional context, 24 though there is little explicit inclusion of the cathode material production step in these material flows outside of one study. 1One recent material flow analysis-adjacent study 66 evaluates the feasibility of meeting the recently passed IRA's goals for minimum critical mineral requirements across all battery materials for the United States, finding that achieving the market value-based target may be possible with NCA batteries but not necessarily for LFP or NMC batteries.We provide an analysis in the context of potential mass-based targets and identify a need for a global perspective.In general, while studies describing the state of supply chains are useful for describing the structure of material flows and supply chains, allowing for analysis of potential vulnerabilities, none of these studies quantitatively measure the interdependencies between specific technology choices and material mass requirements on specific countries.
Two types of studies have considered different ways to measure relationships between steps of supply chains between production geographies, though not necessarily in the specific definition of vulnerability we have used in this article.The input-output (I/O) literature measures flows of materials, emissions, and other quantities through interconnected industries, sometimes through the perspective of a specific material's or product's supply chain.These models can calculate measures of vulnerability through matrices of relationships between industries or steps of a supply chain, making the assumption that input proportions between each stage or step are fixed. 67While input-output models are typically described in terms of one unit (e.g.dollars), a subset of this literature, known as a 'mixed-unit' input-output technique, have focused on combining I/O models with material flow analysis, using mass balance to measure physical flows of materials and sometimes energy or emissions. 68These studies track material flows in detail across steps of the supply chain, but they rely on proportionality constants and thus can only provide point-estimate snapshots of vulnerability on certain geographies.Furthermore, there has been little study of battery material supply chains with input-output analysis, with existing studies focusing on either just lithium-ion battery manufacturing 48 or in non-lithium-ion contexts. 49,50her studies have focused on 'supply chain disruption propagation' for certain battery materials, such as natural graphite, 53 cobalt ores, 54 lithium carbonate and lithium batteries, 51 and nickel. 52These studies calculate the 'avalanche size' of a disruption -the number of countries affected by the removal of supply or trade from one country -while assuming that disruptions occur as proportional losses of trade from the disrupted country that are propagated to other countries.Most of these studies underscore the significance of China as a critical node in the supply chain though these studies are limited to specific trade codes or materials.Furthermore, all of these studies except the study on nickel do not consider the fact that there are relationships between countries at multiple steps of the supply chain, and the nickel study uses a correlation instead of considering the actual physical quantities of materials that are converted from one step of the supply chain to the next.While this measure of vulnerability may be helpful in understanding linkages between countries, we suggest that the lack of analysis across multiple materials and the physical quantities of materials needed constitutes a gap in the literature.
As summarized in Supplementary Table 5, no existing models incorporate these six primary qualities, so we create a new model, leveraging prior work and bridging these gaps, to answer this question.We work backwards from lithium ion battery cathode material requirements to map the entire supply chain on a country-by-country basis, with awareness of the specific amount of constituent materials needed for each cathode material.We measure overall vulnerability on any given country, going beyond the proportional measurements found in the input-output and supply chain disruption propagation literatures by bounding the possible range of disruption on any given region of interest in the supply chain.

Supplementary Text S3. Full Methodology and Data
Supplementary Text S3-1.Methods

Data Aggregation
We model the supply chain for each chemistry by considering supply of each material for each battery chemistry, focusing on mining, refining, and cathode material production.Each country can produce, import, and export material at multiple steps in the supply chain, and thus the portion of end cathode material that involves a given country in the supply chain varies depending on the amount of end material being produced and the trade relationships between all countries.
While the supply chain for each material can be complex, we make a number of simplifying assumptions given the data available (see Supplementary Fig. 1 and Supplementary Fig. 2).We do not incorporate stages after battery cathode material manufacturing, but include the movement of scrap, with the caveat that little of it is currently involved in the electric vehicle battery supply chain (most nickel and manganese scrap is used in the iron and steel market, 24,65,69 while cobalt scrap is largely from superalloys 46,70 ).Additionally, we generally make the assumption that no firm-level buffers/national stockpiles of these materials exist or are minimal in size relative to trade and/or production.
We aim to represent the flow of materials via trade and processing as a two-dimensional network.We do this by assuming that countries with known production are the only countries with the technological production capability to produce materials at each step, and that no one else has this capability and thus must trade from these producers in order to get these materials.
We track five battery material supply chains: the lithium in LFP cathode materials, and the lithium, nickel, cobalt, and manganese in NMC cathode materials.For each step of the supply chain, we compute a mass balance: Supplementary Equation 1.Total Demand (Demand+Exports) = Total Supply (Production+Imports), for all materials and countries where D mi is the mass of material m used to make all potential products in country i, T mij is the amount of material m traded from country i to country j, J is the set of all countries, and S mi is the mass of material m produced in country i.This equation holds for each material m∈ M={Li,Ni,Co,Mn} and each country i J. ∈ Total trade between countries may involve some trade that is observable and some trade that is unobservable due to smuggling, unintentional misclassification, tariff avoidance, and other reasons. 3,46,71We represent these as follows:  2. Total Imports = Imports from Producing Countries + Imports from Non-Producing Countries + Unobserved Imports, for all materials and countries where T OBS mji is the observed trade from country j to country i available in the data, is the    subset of countries that are known to produce material m, and T UNOBS mi is unobserved trade of material m to country i that is missing in the data.We compute the net value of T UNOBS mi (positive or negative) needed to satisfy Supplementary Equation 1 for each material, country pair, effectively assuming that any mismatch between supply and demand in the data is explained by unobserved trade.The countries that export relevant materials but are not known to have production may obfuscate the true 'original source' of the material, assuming the countries listed with production capacity are the only ones that have the technological capability.This creates additional uncertainty.We can measure the variables in Supplementary Equation 6in terms of demand for cathode materials that require refined minerals.These refined minerals in turn require raw minerals, so we have a two step process, where the total supply of refined materials S mi in the refining-cathode material flow analysis is a subset of the products considered in the total demand for refined materials D mip in the mining-refining material flow analysis.

Vulnerability Analysis and Uncertainty Bounds
We calculate the total vulnerability of cathode material supply for a set of countries, which we designate as the countries of focus.Clearly, any cathode production in these countries would count towards vulnerability due to those countries.However, other countries that produce cathode material could potentially also be vulnerable to the countries of focus for refined materials, while the countries that supply those cathode material producing countries with refined materials could also be dependent on the countries of focus for raw materials.Taking into account this 'ripple effect' across multiple supply flows, we determine the quantity of cathode material dependent on our countries of focus across cathode material production, materials refining, and raw materials production.
To bound this analysis, we consider both uncertainty due to observability of trade between countries that goes to battery end-products, and uncertainty due to unobserved trade data: trade that should exist in order to produce battery products but otherwise is unobserved in the trade data.Using these, we measure the amount of vulnerability based on a country in four ways.
In a proportional trade case, we find the total amount of internal supply less exports, and the total amount of imports for each country with production capability at each step.With this data, we can calculate the percentage of supply at each step that depends on the countries of focus.By aggregating these percentages at each stage of production, we can calculate an overall percentage of the end cathode production that becomes unavailable.In this scenario, we assume any unobserved trade follows the same patterns as observed trade.8,[72][73][74] The other three vulnerability calculations use the concept of maximum flow 75  node where all mined and raw material originates from, with capacity equal to the amount of production claimed by each raw material producing country.
In a maximum known trade case, we try to optimize the flow of material across our network, such that as much of it passes through the countries of focus as possible.By connecting the supersource node to all of the countries of focus at each step of the supply chain, with effectively infinite capacity in these flows, we can apply a maximum flow algorithm (in this case the Edmonds-Karp algorithm 76 ) to calculate the maximum vulnerability based on the countries of focus.Through careful analysis of the distribution of flows using the outputs of the algorithm, we can determine the vulnerability at each step of the supply chain.
To understand the impact of unobserved trade in the maximum trade case, we assume it could all come from the countries of focus.In practice, we connect the nodes that represent uncertain supply (MMRS, TCNM, UARP, TCNR, MRMC) to the supersource, to include them as potential sources of material.However, not all of these materials can necessarily come from our country of focus if they are not actually known to produce materials in the steps upstream of the uncertain supply, e.g.Russia is not known to be a producer of raw or refined lithium, so none of the uncertain lithium supply should come from Russia.Thus, we include the (still relatively naive) assumption that the maximum flow from our supersource to any of these uncertain supply nodes cannot exceed the sum of the production across all countries of focus at the step that the uncertain supply node joins the material flow network.We assume any of the TCNB and RMRP could have been converted at some point.TNPC is any 'missing' refined materials, while any refined material is not recorded as being used in cathode material manufacturing could have been re-imported or miscategorized A minimum trade case is the same measurement as the pessimistic scenario, but instead chooses the countries that import the least quantities of materials, and further assumes unobserved trade does not come from the country at all (minimal vulnerability based on the country in question).The practical implementation of this is to calculate the inversedetermining the maximum flow through the network where all flows into and out of nodes in the countries of focus are not included in the network, and subtracting that amount from the expected demand at the last (cathode-producing) step to determine the amount of material that at minimum must come from the countries of focus.

Supplementary Text S3-2. Data Sources Production Data (s αi and d pi )
We choose to use 2020 USGS mining data 17 like many other studies in the critical materials and material flow analysis literature. 14,25,46These data are largely reported in terms of contained minerals (e.g.metric tons of lithium equivalent or thousands of tons of nickel equivalent), which reduces uncertainty from needing to use conversion factors, as described below.While there may be some lag in production processes, such as lithium brines requiring up to a year to process via evaporation, 6 USGS production data is reported in terms of final production quantities (e.g. after lithium concentration).We use refined materials and cathode materials production data (as well as US lithium production) reported in Sun et al. 2021, 22 which is largely from 2020.For the analysis of phosphorus included in Supplementary Text S1, given that granular production data for the refining step (phosphoric acid) was not found, we used regional production statistics from IFASTAT, the International Fertilizer Association's statistics website. 30ade Data ( )   β Following methodologies from the material flow analysis literature, [1][2][3][4]23,46,47,65,69,70,[77][78][79] we trace inter-country trade from country to country by identifying relevant Harmonized System (HS) codes. These codes, internatioally standardized by the World Customs Organization to 6 digits, allow for importing countries to levy tariffs and monitor compliance with regulations (e.g.rules of origin), and as such are designed to classify and cover all internationally traded items.80 Most sources of trade data are ultimately based off of the UN Comtrade database, which aggregates reports submitted by UN member countries on their trade at a high level, which is the database used by nearly all global material flow analysis and supply chain disruption propagation studies reviewed in this article.[2][3][4]23,25,46,47,[51][52][53][54]65,70,74,[77][78][79] Other national and regional-level trade databases, such as the US Census's database or Eurostat, are much more detailed, but do not cover the entirety of trade around the world, and as such are less useful when considering whole supply chains.These national and regional databases could be used to supplement data gathered from international sources, which is what is done in the data source we use.It is also important to note that both export and import data exist in these databases.Nearly all reviewed studies in the material flow analysis and supply chain disruption propagation literatures that specified a choice between the two used import data 2,3,46,51,54 rather than export data, 65 as it tends to be more complete and accurate, as many countries impose various import tariffs and are concerned about what materials enter their borders, 2,46,80,81 so we also use reported import data figures.
We use TradeMap data from IntraCen 80 as it provides the UN Comtrade data while additionally supplementing it with national and regional trade where import and export data may be conflicting or missing, as some countries do not report data to UN Comtrade.It is the opinion of the authors that this incorporation of national and regional trade data positively augments the UN Comtrade database upon which most material flow analyses base their analyses on.We use 2020 data to synchronize with our 2020 production data, and as a result rely on the 2017 HS code nomenclature.Databases based on the UN Comtrade dataset report their data in both dollar value and quantities.While using either has its drawbacks (commodities have constantly fluctuating prices and materials imported under trade codes are not homogeneous and not all shipments are accurately weighed and contained amounts of the critical material vary), we chose to use the latter to minimize the impact of uncertainty and issues of propagated errors.This necessitates the use of Conversion Factors (as described in the next subsection) to change the units of the broad categories of each trade stream into terms of contained materials.28 HS codes were selected to represent trade of materials at each stage of the supply chain between mining and cathode manufacturing (see Supplementary Table 7).We reference a variety of literature to fully aggregate across all trade codes that may include battery material supply. 2,20,22,23,25,46,77,82,83ake the assumption that the traded raw and refined material in the selected codes is representative of materials that could actually end up in battery cathode materials.Globally, about 74% of mined lithium 17 and 57% of mined cobalt 84 is used in lithium ion batteries, but only a portion of lithium ion batteries are used in electric vehicles.Furthermore, only about 11% of nickel 85 and 2% of manganese 24 is used to make batteries of any kind.Different grades of ores, refining processes, and precursor materials, including recycled and scrap materials, make it more economically efficient to produce certain types of materials, not all of which can be used for battery cathode material production, and not all battery cathode materials are used in electric vehicles.However, as it is possible to use any of these materials in the electric vehicle battery material supply chain with enough processing, we choose to include all of these trade data in our analysis.The relevant supply chain flows included in our dataset are found in Supplementary Text S1-1 and Supplementary Fig. 2. Additionally, while other studies account for missing trade by exploring country-specific trade codes and known inter-country trade relationships, other than the export of Australian lithium, we do not account for any of these potential clarifications of the missing data problem.
We recognize that this snapshot of a dynamic system is likely not to be perfectly accurate; our inclusion of uncertainty analysis around our primary point estimates attempts to account for these challenges.Additionally, with improved data, we suggest the power of this methodology only increases.

Conversion Factors ( ) 𝑐 β𝑚
In order to map the flows of each material in terms of the actual amounts traded, rather than the numerous compounds containing various amounts of the material, conversion factors are used to standardize all trade in terms of units of contained material.We reference a number of sources for estimates 1,4,22,47,65,86,87 for these coefficients for each trade code (see Supplementary Table 7).We recognize that these are point estimates and therefore possibly uncertain and/or are affected by anchoring bias; the few sources with overlapping trade codes generally agree on these conversion factors (or cite these original studies to begin with).[a]: While most lithium is produced from brines that are refined into lithium hydroxide or lithium carbonate forms near the mining sites, lithium as an ore (which is currently essentially all found as spodumene) is presently only produced in Australia and China 17 and not tracked as a specific commodity in the HS system. 80Noting that only Australia and China have any lithium spodumene ore production, 17 we assume all Chinese production is domestically consumed for refining, and refer to Australia's country-specific export data of "25309011 Lithium concentrates", using the "ores" conversion factor from Sun et al. 2018 to convert it to quantity of contained lithium, to estimate Australian lithium exports.
[b]: The codes 280519, 282690, 282739 are used in lithium-ion batteries, sometimes as lithium alloys, but primarily as inputs for battery electrolytes. 77Because materials covered under these trade codes have an unclear relationship with cathode material production (and cathode materials are already traded under other trade codes), we disclude these from our trade analysis.
[c]: Discluded as it primarily refers to stainless steel waste and scrap [d]: Discluded as it removed in 2007 HS code revision 80 [e]: Discluded as unclear which of cobalt compounds listed would be included, and cobalt content is highly uncertain [f]: Discluded as it removed in 2002 HS code revision 80 [g]: This study 83 mistakes magnesium for manganese and thus this is not included; this code is for magnesium sulfate 80 [h]: Li et al. 87 identify the conversion factor for Phosphorus rock (ground or unground) to be 9.8%.Chen and Chen 86 assume 32% of the weight of phosphate rock is P 2 O 5 , which, using a chemical formula, results in about 14% of the rock as phosphorus.We take the average of these two numbers.We assume the phosphorus content in phosphorus is pure (100%), while for phosphoric acid, we take the average of the values of phosphorus in phosphoric acid calculated from chemical formula (0.316), Li et al. (0.268), and Chen and Chen (0.236).
[i]: Using chemical formulas for LFP (LiFePO 4 ) and NMC622 (LiNi x Mn y Co z O 2 , x+y+z ≈ 1), we find conversion factors of 0.0440 and 0.0716, respectively.Other sources 4 list them as 0.07 and 0.04, respectively, instead; it is possible that they were accidentally swapped in their analysis.We choose to use NMC622 as it is quite close to the average chemical composition based on a predicted market size-weighted blend of NMC technologies, as seen in Supplementary Table 8.This calculation is based on a simulated share of choices presented in a projected LFP-dominant scenario, 88 which is what is currently empirically happening as the electric vehicle market is developing.
Supplementary Table 8.NMC simulated share of choices and representative chemistry analysis. 88 bold NMC622 and the Weighted Average rows to highlight their similarity; we use NMC622 as the rough approximation of the average NMC chemistry to calculate the minimum and maximum vulnerability on any set of focus countries.We translate our Sankey diagrams into network flows.Nodes of the network correspond to the vertical bars in each Sankey diagram at each of the five stages of the diagram -mining, mining post-trade, refining, refining post-trade, and cathode production, while connections in the network correspond to the flows in each Sankey diagram between the stages, representing either trade (internal or international) or material processing between each stage.Furthermore, we add a 'supersource'

Table 2 .
roughly 23.5 million tons of phosphate rock, or about 2.3 A review of the criticality of electric vehicle battery cathode materials.: Yes, N: No, na: not applicable Y metric tons of phosphorus were mined in the United States in 2020; it is clear the United States alone could supply the world's LFP-Phosphorus demand hundreds of times over.For further context, the USGS identified 71 billion metric tons of phosphate rock reserves (i.e.
Y All are named as critical by construction; see Fig.4 and 7. *Only Aluminum is notably 'less critical' in comparison. million

Table 4 .
We see that the measured vulnerability index values are not altogether that different from that of Lithium for LFP: slightly lower in the proportional case and going up to 100% in the 'known trade' pessimistic case.However, we cannot be certain of any measurements beyond the observed production of LFP in the cathode step, as we only observe inter-regional trade and thus cannot be sure if this is actually the vulnerability index for phosphorus and China.
Trade T between countries j and i = Trade t of items  ✕ contained material per item Furthermore, we cannot directly observe the movement of material m in its pure state (e.g.contained nickel compared to nickel ores and concentrates, nickel mattes, nickel sulfates, unwrought nickel alloys, etc.).Assuming no losses in the production processes, we use conversion factors c to convert from input materials α with supply s αi , imported goods β at amount t βji , and demand from produced products d ip to their contained material amounts, S mi , T mji , β Supplementary Equation5.andDmip,asseen in Supplementary Equations 3 through 5.These conversion factors c are described below in the Data Sources section (Supplementary Text S3-2) and compiled with associated trade codes in Supplementary Text S3-3.Values for t βji are associated with relevant trade codes in Supplementary Text S3-3.As a result, combining all unobserved trade into one variable and trade from and to non-producing countries into another, recognizing that quantity can be positive or negative, we describe our total supply-demand balance in Supplementary Equation6.Supplementary Equation6.Total demand for each material = Material supply + (Material imported -Material exported) + Unobserved Trade

Table 6 .
Flow Constraints in the maximum trade case that includes uncertain (unobserved and indirect) trade data